Not able to understand gain in decibels

Discussion in 'Homework Help' started by aman92ullah, Jan 26, 2012.

  1. aman92ullah

    Thread Starter New Member

    Jan 19, 2011
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    I can get s-domain transfer functions, say for a AC coupled inverting amplifer. But I can't quite interpret it, especially when gains are in dB. I know what dB is and can interchange simple gains into dB.
    But when there is a circuit involved, I get confused: how does transfer function map simple voltage gain to dB?
    I was trying to solve a problem(5.25) from sedra and smith(5ed): R1 is 1k, R2 is 1M.(See attached figure)
    Question is that what will be the value of coupling capacitor to ensure gain will be greater than 57dB down to 100Hz.
    I am getting 10uF as answer, while the books says it's 1.6uF. I first found the transfer function, which was: Vo/Vin=(-R2/R1)*(s/(s+(1/R1C1)). I take 20 log on both sides, and solve for c1 putting s=100. Where am I wrong? Or my entire concept is botched?
    Help!!
    [​IMG]
     
    Last edited: Jan 26, 2012
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    It appears the attachment didn't make it with your post.
     
  3. aman92ullah

    Thread Starter New Member

    Jan 19, 2011
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    I have uploaded the file now. (Sorry, first time around here. Learning)
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    There's no need even to consider the 's' domain transform of the circuit.

    A gain of 57dB is equivalent to a straight voltage gain of 707.95.

    The amplifier gain will be given by

    A_v=\frac{R_2}{|Z_{in}|}

    where

    |Z_{in}|=\sqrt{R_1^2+X_c^2}

    If Av=707.95 and R2=1MΩ

    then |Zin|=R2/Av=1MΩ/707.95=1412.5Ω

    One then uses the second equation above to solve for Xc & hence C given
    R1=1000Ω & |Zin|=1412.5Ω
     
    aman92ullah likes this.
  5. aman92ullah

    Thread Starter New Member

    Jan 19, 2011
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    Well, that's all right. Thanks!
    But I am still stuck with the 's' domain. When we put the gain in dB, we say
    Gain(dB)=20log(Vo(s)/Vin(s)) =(X)provided impedances match. My question is, what is X in the s-domain? Isn't it what I wrote in the first post?
    Sorry, it might be very stupid, but I am struggling with s-domain and bode plots for some time now. Please!
     
  6. aman92ullah

    Thread Starter New Member

    Jan 19, 2011
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    My problems with s-domain notwithstanding, I found the error! Actually I was putting ω=100hz, while ω=2πf. Now I'm getting the answer 1.6uF from s-domain as well.
    Thanks again for your time!
     
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